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Robust Standard Errors for Robust Estimators

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  • Christophe Croux
  • Geert Dhaene
  • Dirk Hoorelbeke

Abstract

A regression estimator is said to be robust if it is still reliable in the presence of outliers. On the other hand, its standard error is said to be robust if it is still reliable when the regression errors are autocorrelated and/or heteroskedastic. This paper shows how robust standard errors can be computed for several robust estimators of regression, including MMestimators. The improvement relative to non-robust standard errors is illustrated by means of large-sample bias calculations, simulations, and a real data example. It turns out that non-robust standard errors of robust estimators may be severely biased. However, if autocorrelation and heteroscedasticity are absent, non-robust standard errors are more e.cient than the robust standard errors that we propose. We therefore also present a test of the hypothesis that the robust and non-robust standard errors have the same probability limit.

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Bibliographic Info

Paper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces0316.

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Date of creation: Mar 2003
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Handle: RePEc:ete:ceswps:ces0316

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Keywords: robust regression; robust standard errors; autocorrelation; heteroskedasticity;

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Cited by:
  1. Markus Baldauf & J.M.C. Santos Silva, 2009. "On the use of robust regression in econometrics," Economics Discussion Papers 664, University of Essex, Department of Economics.
  2. Rodolphe Desbordes & Vincenzo Verardi, 2011. "The Positive Causal Impact of Foreign Direct Investment on Productivity: A Not So Typical Relationship," Working Papers 1106, University of Strathclyde Business School, Department of Economics.
  3. Andreas Alfons & Wolfgang Baaske & Peter Filzmoser & Wolfgang Mader & Roland Wieser, 2011. "Robust variable selection with application to quality of life research," Statistical Methods and Applications, Springer, vol. 20(1), pages 65-82, March.
  4. Robert Finger, 2010. "Revisiting the Evaluation of Robust Regression Techniques for Crop Yield Data Detrending," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(1), pages 205-211.
  5. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods and Applications, Springer, vol. 17(1), pages 41-71, February.
  6. Catherine Dehon & Marjorie Gassner & Vincenzo Verardi, 2011. "Extending the Hausman Test to Check for the presence of Outliers," Working Papers ECARES ECARES 2011-036, ULB -- Universite Libre de Bruxelles.
  7. Marek Omelka & Matías Salibián-Barrera, 2010. "Uniform asymptotics for S- and MM-regression estimators," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(5), pages 897-927, October.

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